(2x%2B1)%3Dx(x%2B5)-solution.jpeg "(x-3)(2x+1)=x(x+5) Solution")
Solving the Equation (x-3)(2x+1)=x(x+5)
This article will guide you through the steps of solving the equation (x-3)(2x+1)=x(x+5).
1. Expanding the Equation
First, we need to expand both sides of the equation by multiplying the terms:
- Left side: (x-3)(2x+1) = 2x² - 5x - 3
- Right side: x(x+5) = x² + 5x
Now, our equation looks like this: 2x² - 5x - 3 = x² + 5x
2. Simplifying the Equation
To make the equation easier to solve, we'll bring all the terms to one side:
- Subtract x² from both sides: x² - 5x - 3 = 5x
- Subtract 5x from both sides: x² - 10x - 3 = 0
3. Solving the Quadratic Equation
We now have a quadratic equation in the form of ax² + bx + c = 0. We can solve this using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
In our equation:
- a = 1
- b = -10
- c = -3
Substituting these values into the quadratic formula:
x = (10 ± √((-10)² - 4 * 1 * -3)) / (2 * 1) x = (10 ± √(112)) / 2 x = (10 ± 4√7) / 2
Simplifying the solution:
x = 5 ± 2√7
4. The Solutions
Therefore, the solutions to the equation (x-3)(2x+1)=x(x+5) are:
- x = 5 + 2√7
- x = 5 - 2√7